Equalization, or filtering, is used to alter the frequency spectrum of a signal by altering the frequency response of an equalization device through which the signal passes, e.g. by increasing or decreasing the amplitude of the signal over a band of frequencies while leaving the amplitude of the signal at other frequencies largely unchanged. The signal may be a digital audio signal, but it will be appreciated that it may be other types of signal too. The filtering is achieved by processing the input signal such that the output signal from the filter depends upon some constant linear combination of delayed samples of both the input signal and the output signal of the filter. In general the filtering of a signal to produce a desired frequency response has the side effect of also causing a frequency-dependent change in the delay imposed upon the signal. When this delay at a particular frequency is viewed in comparison to the period of that frequency this can be seen as a phase difference.
It is known to construct FIR (finite impulse response) filters of arbitrary frequency response and arbitrary phase response, particularly FIR filters of linear phase, i.e. those that have constant delay regardless of frequency. However FIR filters have disadvantages when used for audio equalization, in that they are very much more complex, more difficult to control and have greater delay than IIR (infinite impulse response) filters.
In general small changes in phase are not audible. However, a problem with phase shift occurs when two versions of the same signal, but with different phases, are combined or added together. When this happens, the frequency-dependent difference in relative phases between the two versions causes undesirable and unintended filtering effects.
For many applications a true linear phase, constant delay filter (which can only be a symmetrical FIR filter) is not what is required. Instead, for many applications the actual requirement is that multiple independently equalized signals be made from a single input signal, and that all output signals have identical phase responses. This is the requirement when the multiple output signals may later be additively combined in an arbitrary manner.
One example application is in the control of “line array” loudspeakers used for public address in large venues. These line arrays use the constructive interference between vertically spaced elements to control their directional properties, thus it is important not to disturb the relative phases of the individual elements in the array. On the other hand it is frequently required that different equalization be applied to different elements of the array which are responsible for delivering sound to different areas of the audience. Typically the top elements in the array deliver sound to the back of the auditorium while the lower elements deliver sound to the front of the audience. The large difference between the distances served by the top of the array and by the bottom of the array means that it is frequently required to apply different equalization to the different elements in order to counteract the high-frequency attenuation of the longer path lengths. Thus the equalization of these arrays requires multiple, different, frequency responses to be imposed on individual outputs without them having different phase responses and all with low delay and low computational complexity.
A second application can occur in loudspeakers designed for domestic sound reproduction. Frequently more than one transducer is present in a single cabinet and this can lead to similar constraints to those mentioned above.
A third application occurs in consumer audio equipment where it is desired to allow the user to alter the frequency response of some element of an audio system using a simple cross-fade control between signals which have been exposed to two extremes of filtering. Typically a signal may be constructed with increased bass response, and another with increased treble response, and a simple selection of a weighted sum of these two signals will be used as the final output with the relative weighting under control of the listener. Such user control can only be achieved in this manner if the two signals are in phase throughout the audio band.
It will be appreciated that other example applications exist that require generating multiple independently equalized signals from a single input signal, where all of these generated signals have identical phase responses.